Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
The torque created using an oval chain ring I have seen the explanation on "How bicycle gear works?" but this seem to be using a standard round chain ring. I would like to know if there is any difference when an oval chain ring is used. As I can clearly see, one can have an oval chain ring on a fixed/single gear bike. ... | The principal benefit of elliptical chainrings is to reduce the resisting torque when the pedals are oriented vertically (one foot higher than the other) and increase the generated torque when the pedals are oriented horizontally (both feet at the same height). This is because a person can produce much more torque in t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How do we know the number of photons in a decay? How can we determine the exact number of photons produced in a decay or other event? This has puzzled me because photons can have arbitrarily low energy and momentum, so how do we tell if two photons are produced or three photons one of which has arbitrarily low energy? ... |
how do experimentalists distinguish between the number of photons produced in a decay or other event?
By designing an experiment that can detect photon direction and energies of the photon , and using previously established conservation laws , energy, momentum, and quantum numbers to interpret the data.
because pho... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/317962",
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Induced electric field in circular wire around solenoid I have a stationary solenoid of radius $a$ and length $L$ with $n$ windings per unit length. There is a time varying current in the wire $I = kt$, with $k$ a constant. A conducting wire with radius $r$, mass $m$ and resistance $R$ is placed around the wire centred... | Inside the solenoid:
The field is $$B(t)=\mu_0ni(t)$$
So for $r<a$ the flux is $$\phi_B=\mu_0ni(t)*\pi r^2$$
$$\oint E\,ds=\frac{d\phi_B}{dt}$$
$$E2\pi r=\mu_0nk\pi r^2$$
$$E=\frac{\mu_0nkr}{2}$$
Outside the solenoid:
$$B=0$$
So the magnetic flux is only due to the field inside the solenoid:
$$\phi_B=\mu_0ni(t)*\pi a^2... | {
"language": "en",
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Low power loss in electricity transmission lines To reduce the heat lost during transmission of electricity, we say we increase the voltage of transmission, taking the formula $I^2R$ in consideration. Couldn't I consider $V^2/R$? If I consider the second form, increasing voltage will increase the power dissipated. No?
| $P = I^2R$ gives the power consumed by the transmission lines if $I$ is the current through the transmission line and $R$ is the resistance of the transmission line.
$P = \frac{V^2}{R}$ gives the power consumed by the transmission lines if $V$ is the voltage across the transmission line only and $R$ is the resistance o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/318230",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What does it mean by "an atom at rest"? I was reading a document when an article about atomic clock passed by. There is statement that I don't understand
The second is the duration of 9 192 631 770 periods of the radiation
corresponding to the transition between the two hyperfine levels of the
ground state of the ... | In this context, "at rest" means in a reference frame centered at the atom.
In practice, you can't get any system to exactly 0 K, nor can you make an observation from directly on the atom.
But, you can plot the periods of radiation relative to temperatures that are very low and to make any necessary special relativis... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/318366",
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Can a neutrino antenna be made one day? I am wondering if it is theoretically possible that some kind of device/material could absorb neutrinos much better than everyday materials (preferably non-thermal absorption). This could enable a sort of neutrino antenna.
| How does an electromagnetic antenna work at the photon, quantum mechanical level? By inducing varying electric fields which induce accelerated charges which radiate coherently photons which build the classical electromagnetic wave.
The neutrino interacts with the weak interaction , is a fermion and can in no way be i... | {
"language": "en",
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Why doesn't saturation current in the photoelectric effect depend on the frequency of light absorbed by the metal emitter? If current $I$ is given by $I = nAev$, where $n$ is the number of electrons per unit volume, $A$ is the area, $e$ is the charge of an electron and $v$ is the velocity of the electron, it must mean ... | Well in the equation $I=neAV$ with the increase in $V$, $I$ increases only if n, e, A does not decrease . Now just think if you increase the drift velocity of the electron then they would move from their position and the no of electrons per unit volume (n) should decrease. Thus the resultant effect is that I does not ... | {
"language": "en",
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Halbach array and levitation Full disclosure: I am a total novice when it comes to physics apart from being very curious and basic physics classes at school level (long long ago).
Using 16 mm diameter disc magnets. I am attempting to make a magnetic track and levitating vehicle. First tries quickly taught me that the i... | The only stable ferromagnetic system I know is the "Levitron", which levitates a spinning magnet. That might not be suitable for your project. So instead you can use rollers or air bearings to the sides of your vehicle to provide stability. Those rollers/bearings would not need to support the weight of the vehicle; ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/318948",
"timestamp": "2023-03-29T00:00:00",
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How does one measure the curvature $k$ in FLRW metric? How does one measure the curvature parameter $k$ in the FLRW metric? $$ds^2=-c^2dt^2+a^2(t)[\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2\sin^2\theta d\phi^2]$$ In particular, what is the convenient equation (involving $k$) that is/can be used to measure $k$?
EDIT I'm look... | You simply measure the ratio of the circumference of a circle to its radius.
Take a spatial submanifold, and for convenience we'll take $a=1$ (the units of the radial distance can always be chosen to make $a=1$ as any chosen time). Then the spatial metric becomes:
$$ d\ell^2=\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2\sin^2\t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/319124",
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"question_score": "3",
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How is entropy a state function? Is there only one reversible way to move from one state to another?
If we consider two states $A$ and $B$ on an isotherm and we move from $A$ to $B$ by first reversible isochoric process and then reversible isobaric process. Now the path followed should be reversible since both the ... | Your question goes right in the kernel of the meaning of the term state function.
A state function is a function defined over all possible states of the system such that its value for every state does not depend on how the system reached the state. Each state has a definite and unique value for the given state function... | {
"language": "en",
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How a moving car becomes electrically charged? Car has been electrically charged as it travels along the road.how is this possible?
| Look up Triboelectricity.
When objects come into contact with one another, temporary chemical bonds form between the touching objects. When these are afterwards broken mechanically, they can leave the two objects with an surfeit / dearth of electrons on either side of the broken bond.
This process happens continuously... | {
"language": "en",
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Misconceptions on Electronics and circuits So i had a question regarding basic circuits
*
*What do negative currents and voltages mean.? This really stumped me for a while as negative current and voltage seemed odd to me if someone can clarify much appreciated.
p.s Sorry didn't realise there was too many questio... | *
*Power dissipated in a resistor $R$ is $I^2R$
*Positive charges can also contribute to the current in gasses. Only electrons can move in a solid conductor.
*What do you mean by 'just a wire'. Does your wire have resistance?
*Yes, A is at a higher electric potential than B. It's the result of chemical reactions in... | {
"language": "en",
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Rotation by a given distance in given direction on a Bloch sphere I'm using the following matrix to rotate a states by a distance given by $\theta$ in a direction given by $\phi$:
$$
U = \left(\begin{array}{cc} \cos{\theta\over{2}} & -e^{- i\phi}\sin{\theta\over{2}} \\ e^{i\phi}\sin{\theta\over{2}} & \cos{\theta\over... |
when I do it for any other state, e.g. $|+\rangle$ - distance between two states after that operation isn't always equal to $\theta$ and depends on $\phi$ parameter.
That's the expected behaviour. Every rotation of the Bloch sphere has stationary points (or, in Hilbert-space language, every unitary has a basis of eig... | {
"language": "en",
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Why does a laboratory centrifuge cause heavier particles to go to the bottom of the tube? From what I have read online, I can understand that there is a "centrifugal force" that pushes the heavier objects away from the center, but I cannot understand why.
I asked my teacher and she told me that I have to think about w... | It is not mass but density which is the important parameter.
What you have is a "local" value of $g$, the "gravitational field strength" which is $R \omega^2$ where $R$ is the radius of the orbit and $\omega$ is the angular speed - this provides your centrifugal force which is the weight of a mass in this local gravita... | {
"language": "en",
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"source": "stackexchange",
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Photoelectric effect:- Reduction of wavelength increases current? I did a question in which, the intensity of the incident radiation on a metal surface was kept constant but the wavelength of the photons has been reduced. The question inquired what will be the effect on the maximum photoelectric current? The initial wa... | Intensity of light means total energy per unit time per unit area.As in later case wavelenght of light was decreased so the energy of individual photon will increases but the intensity was kept constant so there should Be less number of photon falling per unit time per unit area.Just remember intensity of light is not ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/320533",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is the existence of a photon relative? If an observer passes an electron, in such a way that the observer is accelerating, the observer would see photons because accelerating charges induce electromagnetic waves.
But from point of view of the electron or an inertial observer there is no magnetic field nor an accelerat... | The short answer is yes. When one tries to generalise the theory of quantum fields in Minkowski spacetime to more general spacetimes, one finds that several familiar features of the theory are absent or ambiguous. For instance, it is not generally possible to unambiguously define a vacuum state when studying QFT in a c... | {
"language": "en",
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Why is the mol a fundamental physical quantity? I am starting to study physics in detail and as I read about physical quantities, I was puzzled why mol (amount of substance) is taken as a physical quantity.
A physical quantity is any quantity which we can measure and has a unit associated with it. But a mol represents ... | Is it a fundamental number in nature? It's (currently) a number resulting from atomic structure (fundamentally defined by the masses of quarks, Planck's constant and the way quantum mechanics works) and our definition of the gram, which is based on the international Kg prototype. Avogadro's constant is currently define... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/320784",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Adiabatic free expansion of real (Van der Waal's model) gas below/at/above inversion temperature For an adiabatic free expansion, $W = 0$ and $Q=0$. Therefore, by the first law of thermodynamics, $\Delta U = Q -W = 0$.
For a Van der Waals model of a real gas, $\Delta U = n C_v \Delta T - a\,n^2 \left(\frac{1}{V_2}-\fra... | Your calculation indeed shows that the temperature of the van der Waals gas always decreases in adiabatic free expansion. It is only when the gas flows between two regions of different pressures that the sign of the variation of temperature depends on the temperature. Enthalpy, rather than energy, is conserved in this ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/321055",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Uncertainty: $f(n) = K \log n$? I've been searching for the derivation of Shannon's info theory derivation and I landed upon this page from Stanford:
http://micro.stanford.edu/~caiwei/me334/Chap7_Entropy_v04.pdf
They've repeated referenced formulas (page 9) like $f(n) = K \log n$, $f(mn) = f(m)+f(n)$ where $f$ seems to... | These aren't referenced equations. These are equations which are logically derived from the above text.
(The rest of the answer references the text -- I will put another link here for convenience: http://micro.stanford.edu/~caiwei/me334/Chap7_Entropy_v04.pdf.)
Let's try to go through the logic. Equation (9) simply defi... | {
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Miller indices vs Laue indices? I am looking at the difference between the Miller indices and Laue indices in crystal structures. I will denote the former by $hkl$ and the latter by $HKL$.
I understand that $hkl$ must be coprime integers, however, I have also heard that $hkl$ represent families of lattice planes. For ... | The distinction between the two indices is quite subtle.Perhaps it is better to start from the laue condition. Let's say I have rows of atoms with spacing $a$. We are in the fraunhofer limit so when two x-ray beams come in and scatter off neighboring atoms they come in parallel and go out parallel. We can then consider... | {
"language": "en",
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if white things reflect light and mirror reflect light why don't they look the same We learned at school that white object reflects all the light that falls on it. We also learned that a mirror reflects all light as well. However, we cannot see ourselves in a white object while we can see ourselves in a mirror.
What m... | A white object only appears white if white light is striking it. If only red light is striking it, it appears red. A mirror has less distortion than other surfaces so it reflects light in a straight line. You don't see the surface of the mirror but rather the objects from which the light originates.
NB, when I speak a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/321357",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Kinetic, potential and total orbital energy in General Relativity In Schwarzschild geodesics the total orbital energy $E$ is
$$E = \dot{t} \left( 1 - \frac{r_{\rm s}}{r} \right) m \, c^2$$
with the time dilation factor $\dot{t}$ in dependence of the local velcity $v$
$$\dot{t} = \frac{1}{\sqrt{ \left( 1-\frac{r_{\rm s}... | Your expression for the total energy can be written as:
$$E=mc^2\frac{\sqrt{1-\frac{2GM}{rc^2}}}{\sqrt{1-\frac{v^2}{c^2}}}$$
This is slightly wrong because in general relativity under spherical symmetry you have:
$v_{light}=c(1-\frac{2GM}{rc^2})$
in the radial direction and:
$v_{light}=c\sqrt{1-\frac{2GM}{rc^2}}$
in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/321481",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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For a tall skyscraper, what are the requirements for young/shear modulus? I am teaching physics 101 for the first time and am discussing stress/strain. As an illustrative example to students, I'd like to make the broad statement, "The primary supports in skyscrapers need a high Young's modulus (to support the structure... | You are confusing the modulus of a material, with the stiffness of an object made from that material.
Let's assume the skyscraper has a steel frame. Steel is isotropic, so like all isotropic materials, there is an equation linking its Youngs modulus, shear modulus, and Poisson's ratio: $$E = 2G(1 + \nu).$$
Since for mo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/321598",
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Why do all electromagnetic waves travel at the same speed when travelling through vacuum? What does my teacher mean when he says that all electromagnetic waves travel at the same speed when travelling through a vacuum? If you may, please answer as simple as possible.
| Assume you are walking down the road. You carry a little stick with you. Just for fun you decide to wiggle the stick rhythmically up and down at the rate of one up/down wiggle per second (you are a bit of an olympic expert at stick wiggling so it's very accurate and reliable). Your stick wiggling is at 1Hz. The speed a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/321667",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Multiple star system, stable orbits? Inspired by worldbuilding SE, I know that there are relatively stable star systems with two or three suns, but any more than that and they start to become very unstable (e.g. trapezium systems), but I'm more interested in the concept of >3 stars, each of similar mass. How could they... | If space is not a concern (so no perturbations from the outside) then there should be no limit on the number of stars. Because you can always take a duplicate of your current system place them in orbit of each other far enough apart from each other such that the tidal perturbations can be neglected.
Instead of doubling... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/321760",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does Earth experience any significant, measurable time dilation at perihelion? Is there any measurable time dilation when Earth reaches perihelion? Can we measure such a phenomena relative to the motion of the outer planets?
| The GPS depends on corrections to the timing from General and Special relativity because the satellites are in a smaller gravitational field and they are running with a high enough velocity.
Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/321910",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does the proton have a parity $P=1$ and an anti-symmetric wave function? The overall parity of a proton is 1 because the parity of a quark is 1. How does this go together with the proton's wave function being anti-symmetric?
Is the reason for the proton's wave function's anti-symmetry the fact that in $SU(3)_C$ you... | The spin-flavor part of the proton wavefunction,
$$
|p_\uparrow\rangle= \frac{1}{\sqrt {18}} [ 2| u_\uparrow d_\downarrow u_\uparrow \rangle + 2| u_\uparrow u_\uparrow d_\downarrow \rangle +2| d_\downarrow u_\uparrow u_\uparrow \rangle \\ - | u_\uparrow u_\downarrow d_\uparrow\rangle -| u_\uparrow d_\uparrow u_\do... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/322042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is the speed of light the only speed that exists? Well, it seems to me that if I move faster in space I move slower in the dimension of time which is orthogonal to the dimension of space.
All speeds are then equal. Is this statement correct?
| My answer incorporates features of the earlier answers, but tries to clearly disentangle the implied uses of "speed" in space and in spacetime [when a phrase like 'slower in the dimension of time' is used].
"Massive objects (like a basketball) all move at constant 'speed' c in spacetime"
really means that
*
*its 4-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/322145",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can plasma retain a magnetic field? even for the tiniest fraction of a second? If I subject plasma to a magnetic field, can it retain that field after the magnetic field suddenly ceases(the magnetic field disappears is a planck second)
for even the tiniest fraction of a second is the plasma "ferromagnetic"?
| The magnetic field in a conductor (such as a plasma) obeys a version of the diffusion equation:
$$
\frac{1}{\mu_0 \sigma} \nabla^2 \vec{B} = \frac{\partial \vec{B}}{\partial t}
$$
where we have assumed negligible magnetic susceptibility ($\mu \approx \mu_0$) and uniform conductivity $\sigma$. This means that if we cre... | {
"language": "en",
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Why does the Redfield equation model thermal relaxation while the Lindblad equation does not? In open quantum systems, we model a process known as thermal relaxation. What is this process, and why is it that only the Redfield equation models this process, and the Lindblad equation doesn't?
| In open quantum systems, the evolution of the total System is unitary. The freedom degrees of the environment is large, so we always think the environment will not evolve and that is the Born approximation.$$\rho(t) = \rho_{s}(t)\otimes\rho_{E}$$ The relaxation time means the time what the environment need back to equi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/322528",
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Is a mirror-less telescope possible? I was reading about telescopes and the Hubble Telescope for example has a 2.4m mirror which reflects lights to a sensor. Other type of telescopes use lenses to focus light to the imaging sensor.
I was wondering, is it possible to have a telescope without a mirror or lens?
So in Hubb... | A phase(d) array antenna is an imaging device without either a mirror or a lens. Of course, it needs a reference oscillator that is phase coherent with the incoming wave so when the two are mixed in the array, sensor element by sensor element, only the I and Q ("inphase" and "quadrature") components of the incoming wav... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Goldstone bosons, quark and gluon masses counting in color-flavor locking QCD Consider QCD, with three flavors of massless quarks, we like to focus on the possible Cooper paired phases.
For 3 quarks $(u,c,d)$ and 3 colors $(r,g,b)$, the Cooper pairs cannot be flavor singlets, and both color and flavor symmetries are br... | These questions are answered in the original literature:
1) All quarks are gapped. The nine quarks arrange themselves into an octet with gap $\Delta$ and a singlet with gap $2\Delta$.
2) All gluons are gapped.
3) There is an octet of Goldstone bosons related to chiral symmetry breaking, and a singlet associated with ... | {
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"url": "https://physics.stackexchange.com/questions/322952",
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Zero momentum frame in special relativity I am considering a case of collision in special relativity in which there is a change in the number of particles; for example, two particles colliding and sticking together to form a single particle. I was thinking about approaching a problem like this from the zero momentum fr... | Like @Ofek Gillon said, it is about conservation of momentum. In any frame it is conserved, so in the ZM frame before it is 0, after the collision in that same frame it is also zero. Both ZM frames are the same.
A lot of collision physics experiments are analyzed this way because it can be simpler, and after if one ne... | {
"language": "en",
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What determines how much power goes into each diffraction order? Imagine a grating with infinite number of slits, and the spacing D between slits is larger than the wavelength so that there are high order diffractions. In each of the diffraction directions the waves constructively interfere, but what decides the percen... | The physical setup is:
$$
\text{light source}
\quad
\overset{\mathcal{F}}{\underset{\text{(far field)}}{\Longrightarrow}}
\quad
\text{grating}
\quad
\overset{\mathcal{F}}{\underset{\text{(far field)}}{\Longrightarrow}}
\quad
\text{observation screen}
$$
where $\mathcal{F}$ denotes Fourier transform, as known in Fourier... | {
"language": "en",
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If pressure is proportional to temperature, why aren't compressed gases always hot? When you compress a gas, say within a deodorant can, it temporarily heats up, but then cools to room temperature whilst in the can. It will then cool down to below room temperature once decompressed.
It seems like the gas equation doesn... | When you compress a gas into a deodorant can it does indeed heat up. Then if you let the can cool the pressure falls again. The pressure and temperature will remain related by (approximately) the ideal gas law:
$$ P = \frac{nR}{V}\,T $$
You say in your question:
It seems like the gas equation doesn't apply when the ga... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why during annihilation of an electron and positron 2 gamma rays are produced instead of 1? $1 \gamma \rightarrow 1 e^- + 1 e^+$ (pair production)
Then why
$1 e^- + 1 e^+ \rightarrow 2 \gamma$ (annihilation of matter)
instead of
$1 e^- + 1 e^+ -> 1 \gamma$ ?
| This has a simple answer: the process $e^++e^-\to\gamma$ cannot satisfy both momentum and energy conservation at the same time. To see, this let's choose a reference frame in which the total momentum of the system is zero (that is, the electron has the opposite momentum to the positron). This reference frame is always ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Motion of bodies connected by springs Two blocks $A$ and $B$ of masses $m$ are connected by a spring of length $L$ and spring constant $k$. They rest on the frictionless floor. Another body of mass m moving with velocity $v$ collides elastically with $A$. The spring compresses and at maximum compression velocity of bot... | Assuming that the collision takes place over a period of time much shorter than the period of oscillation of the two mass & spring system the collision can be treated as the moving mass, velocity $v$ mass $m$, hitting head on a stationary mass of equal mass.
This results in the originally moving mass stopping and the o... | {
"language": "en",
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Is the diffraction pattern of a vertical slit horizontal? I am familiar with the mathematical aspects of single slit diffraction pattern, at the undergraduate level.
Consider the following pictorial representation from the book Optics, by Hecht:
The fact that I find puzzling here is - even though the slit is shown ver... | To observe the diffraction from a slit assume that the vertical dimension of the slit is much larger than its horizontal dimension. To illuminate it you need a line source not a point source otherwise you will get 2-dimensional diffraction pattern not a simple 1-dimensional sinc thing.
The diagram shows that the rays b... | {
"language": "en",
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Solar neutrino momentum flux through Earth According to wikipedia, the sun emits enough neutrinos that the number passing through a square meter of area oriented perpendicular to the sun at Earth distance is around $6.5 \times 10^{14}$ per second.
What is the momentum flux of these neutrinos? If you counted up the mome... | You really only need one more piece of data to finish the problem: the typical solar neutrino has a momentum of a few $\mathrm{MeV}/c \approx 1.5 \times 10^{-21} \,\mathrm{kg \cdot m / s}$.
Multiplying that by the flux you list above gives about $P_\nu \approx 1 \times 10^{-6} \,\mathrm{Pa}$ for the pressure on a neutr... | {
"language": "en",
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Is the Charge on proton is $3.2\times10^{-19}$ greater than that of charge on electron? As the charge on electron is $$e^-=-1.6\times10^{-19}C$$ and charge on proton is $$p^+=+1.6\times10^{-19}C$$
Does this mean that the charge on electron is $3.2\times10^{-19}C$ less than that of charge on proton?
| Negative doesn't necessarily mean less, especially in Physics. In most cases, negatives just represent the opposite direction. Or negatives represent something which has the opposite effect of the positive quantity. People often consider that negatives are less than 0. Yes, we write $-5<0$. But this 'less' is not the t... | {
"language": "en",
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Why can we only "see" reflected light? This is a question thats been bothering me a while. I don't even know if it makes sense or not (like if it is a physics question or becoming a philosophical one). But here it goes. The crux of my question basically is that we all know that we can't see light (like in its photon or... | Well done. You grasp a concept which many can't. The simplest explanation is that we don't see light, we feel light. By light I mean photons, not brightness. We see brightness because it is a visual sensation created by our brain. When our retina detects a photon it sends a message to the brain and the brain interprets... | {
"language": "en",
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Is there a Birkhoff-like theorem for stationary axisymmetric metrics? I know about the theorem by Robinson and Carter about the uniqueness of the Kerr metric in the case of stationary axisymmetric (SA) black holes. Are there any uniqueness theorems like Birkhoff's theorem for stationary axisymmetric metrics?
| *
*Note first of all that $U(1)$ axial symmetry is much smaller than $SO(3)$ spherical symmetry.
*(Let us put the cosmological constant $\Lambda=0$ to zero.) Where as spherically symmetric vacuum solutions are static and there are no spherically symmetric gravitational waves, the axisymmetric vacuum solutions are no... | {
"language": "en",
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Circuit with three capacitors and a switch I have a homework problem where I have a battery connected to a capacitor and a switch that connects the capacitor to 2 others in series/disconnects the circuit from the battery.
The question is:
S is initially closed to the left until c1 is completely charged. Once charged,... | The total charge on $C_1$ ends up distributed across the three capacitors, so that the final voltage on the three of them will be the same.
Now you know that $Q=CV$. When the switch is thrown, the total charge $Q$ is the same, but the capacitance $C$ becomes 5 times greater (10+20+20).
| {
"language": "en",
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Opposite of particle decay I have read about particle decay, a process in which one particle becomes several other particles. However, I have not been able to find much information about its opposite: several particles combining into one particle. Is such a process possible, and if so, under what conditions? For exampl... | Yes, the reverse of the "particle decay" process is possible. The proof of this is the existence of the universe (and us in it). If it were not possible, there would not be molecules, elements, compounds, etc.. The best example of this, is hydrogen (the most abundant element), which is formed by "uniting" protons an... | {
"language": "en",
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How can length be a vector? Length and current both are not vectors. Then how can we assign the vector $l$ to the length of a wire carrying current while calculating for a current carrying conductor in a magnetic field. Also why in Biot—Savart law do we take small length element $dl$ as a vector?
Why is length sometime... | *
*$\vec l$ is displacement (or position), and $l$ is it's magnitude, called distance or length.
You might hear people call displacement for length, because in the next instant they quickly calculate the length. Sloppy words, that's all.
*
*$I$ is defined as the amount of charge passing through a cross section e... | {
"language": "en",
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Current constraints on Dark Matter self-interaction from galactic profiles The self-interaction of dark matter may be small but it cannot be negligible if it is able to dissipate energy to relax into galactic clumps (necessary to explain galaxy rotation curves).
According to some answers in this old question: How Does ... | Dark matter is still hypothetical - name given to excess gravity that can not be explained in terms of known bayionic matter.
Your question assumes proven existence of dark matter, which is not necessarily true.
Properties attributed to dark matter are - transparent, cold, and non-interactive (except via gravity). Thes... | {
"language": "en",
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The direction of the induced electric field Recently I got stuck witht the following problem.
Imagine we have uniform a magnetic field which induction points upwards. The fields strength is steadily decreasing. If we put an iron coil perpendicular to the magnetic induction vector, then, obviously, there will be electr... | I think what is missing in the analysis is the charge carriers that carry the current (i.e. the electrons). Electric field would be indeed there, if there is no coil, but without coil there are no charges that could be affected by this field and consequently there is no current. If the two coils in the image are joined... | {
"language": "en",
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Is light deflected by external electric and magnetic field? I recently read about the Maxwell's laws of Electromagnetic Waves and I found that Light is made up of both Electric and magnetic fields.
So now if i pass the light through a capacitor such that the plates are parallel to the light will the light be deflected?... | Light is not deflected when it passes through a capacitor.
Light is classicly an electromagnetic wave, and visualizing it as the water waves in a pond might help you solve this cognitive dissonance.
In the finite region in which there is a electric field generated by the capacitor, the electric field of the wave and t... | {
"language": "en",
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"source": "stackexchange",
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Why mass & energy bend spacetime? I understand how light / matter bend spacetime but I'd like to understand WHY. Is there some kind of interaction?
| Given that you understand the how part, I guess you also realize that the how part is actually "how much". I mean you realize that what you understand, is the quantitative analysis, not the root cause analysis.
And I agree with you that quantitative analysis does not always reflect on the root cause. But if someone tel... | {
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How to calculate error using logic? The title may seem a bit off topic. I will explain my doubts with an example.
Let there be a situation where we are measuring gravity using the formula
Now, if the least count or error in the measurement of $l$ and $T$ is given, I can easily find the net error or relative error by t... | There's two possible things going on in such a measurement:
a) measure the time taken for $n$ oscillations and then your systematic error will indeed be reduced, e.g. minimum stopwatch interval $ / n$; and
b) do the $n$-oscillation measurement $N$ times to estimate the statistical uncertainty.
As described by the answ... | {
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What is the relation between image velocity, object velocity and mirror velocity? Suppositions used:
Velocity of image = VI
Velocity of object = Vo
Velocity of mirror = VM
I Know the fact that VI=-Vo supposing mirror at rest
and VI=2VM supposing object at rest
Now considering both mirror and object in motion, VI=2V... | I think its for two cases
case I; when object and mirror moves along same direction Vi=2Vm -Vo
case II: when object and mirror are in motion in opposite direction Vi=2Vm + Vo
| {
"language": "en",
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How to deduce the charge of an electron from the charge of an oil drop in the Millikan experiment? In the Millikan experiment we measure the charge of one oil drop. But how can I measure charge of one electron when I’m not sure how many electrons are contained within one oil drop?
| I think the key was that when you measure enough oil drops, you will notice that the charge is always a discrete multiple of some number. So it shows that charge is quantized. With enough data points, you'd see that the smallest charge difference possible is about $1.6\times 10^{-19}$ coulombs.
| {
"language": "en",
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"source": "stackexchange",
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In cosmology, what is meant by a 'scale', e.g. 'scales smaller than the horizon'? I'm currently reading a cosmology textbook, looking at inflation in particular. I have been seeing "scales smaller than the horizon [Hubble length]" or "horizon crossing" in the context of inflation. I'm just wondering what those phrases ... | You're on the right track. Inflation solves, amongst other things, the homogeneity/horizon problem: the problem that distinct patches of the sky are
*
*causally disconnected; but
*the same temperature.
To solve this, the Universe underwent a period of inflation. 'Scales', that is, distances between patches of the... | {
"language": "en",
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Final velocity when falling to the Earth's center Could someone tell me what the final velocity of an object will be if it fell from the Earth's surface to its center (assuming no air resistance). Since it involves a constant changing acceleration due to the object's distance to the Earth's center decreasing, I'm sure... | I make it $7900\ \text{m}\ \text{s}^{-1}.$ This is using Simple Harmonic Motion theory.
| {
"language": "en",
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When the angle of incidence is less than the critical angle, why is some light still reflected? When the angle of incidence is less than the critical angle, why is some light still reflected? When the angle of incidence is greater than the critical all light is reflected, why is not all light transmitted when it's less... | In the general case, there are 3 components, namely, the incident light, refracted light and reflected light. However, when the light is plane polarised along the plane of incidence,one can show using wave theory of light that if $E_I,E_R,E_T$ denotes the amplitudes of incident,reflected and refracted electric fields, ... | {
"language": "en",
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How is it possible to define work for friction in several dimension? I have been taught that, given a force field F, the work done by the force over a certain curve $\gamma$ is defined as the line integral of said field along $\gamma$.
But this makes sense only if force can be written as a function of position, as it i... | For friction with some medium:
From Rayleigh dissipation function you can take the friction as function of velocity, and define it as a gradient (special one) of some scalar field.
$$\vec{f}=\vec{f}(\vec{v})=\vec\nabla_v \:(\mathcal{F})$$
where $\vec\nabla_v$ is defined as follow
$$ \vec\nabla_v =\dfrac{\partial}{\part... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is really the electric field felt in every thing in space? I was wondering if the action/force of the electric field is really felt everywhere. I know it does reduce as you get further, but my thoughts concerned more about materials.
So, I know that the electric field is strictly related to Coulomb's Law, and Coulomb's... | If I understood the question correctly, yes.
Since every material, at least at the scale you seem to be interested, is made up of atoms, which is a collection of (balanced) positive and negative charges, it will "feel" the effects of an electric field, since the charges that constitute the material will "feel" it.
Of c... | {
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What is the difference between $\psi$ and $|\psi\rangle$? My understanding is that $\psi(\vec{r}, t)$ and $|\psi(\vec r,t)\rangle$ are the same thing yet one expressed as a wave function and the other expressed as a vector in the Hilbert space. Is this true? Or is there a deeper difference between the two notations?
| It is convenient to think of $\vert\psi\rangle$ as a vector with components $\langle x\vert\psi\rangle=\psi(x)$ for various values of $x$. If you imagine discrete rather than continuous values of $x$, then the vector $\vert\psi\rangle$ would be the infinite column vector
$$
\left(\begin{array}{c}
\vdots \\
\psi(x_{n-2... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Potential energy for a crystal lattice I would like some help understanding the following passage:
Consider a crystal lattice such that its unit cell has 27 ions arranged such that there are alternative positive and negative ions for same magnitude.
Then the electrical potential of the crystal lattice is just the pote... |
For instance take a ion at the bottom right corner of the crystal, clearly the potential of this ion wrt to a ion in middle and an ion at top left corner of lattice will differ.
The author here is treating the problem as a symmetric one and ignoring the edge effects (i.e. crystal is extremely big). Say you have N ato... | {
"language": "en",
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Why can gluino (superpartner of gluon) have a Majorana mass? I read in a paper by Scott Willenbrock that gluinos can have a Majorana mass although they have SU(3) color symmetry. The explanation was that gluinos transform under the adjoint representation which is real.
Here is my understanding: gluinos are fermions in... | The gauge bosons in QCD are gluons with the
$$
(c_i\bar c_j + c_j\bar c_i)/\sqrt{2},~i(c_j\bar c_i - c_i\bar c_j)/\sqrt{2}
$$
$$
(r\bar r - b\bar b)/\sqrt{2},~(r\bar r + b\bar b - 2g\bar g)/\sqrt{6},
$$
for $c_ i = (r, b, g)$. These gluons are 3 plus 3 as the root space vectors plus 1 plus 1 as the weights, or the dia... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/328609",
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Michelson and Morley experiment time troubles When discussing the Michelson and Morley experiment (as though the aether existed) we say that the different beams of light would take different times to travel the two distances due to the aether wind and so would arrive out of phase.
I'm having a lot of trouble intuitivel... | Suppose the aether is flowing past the Earth at a speed $v$, then when the light is travelling with the flow its net speed is $c+v$ and when it's travelling against the flow the net speed is $c-v$.
We'll call the length of the arm $\ell$, so for the trip with the flow the time taken is:
$$ t_1 = \frac{\ell}{c+v} $$
and... | {
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Heisenberg uncertainty principle: If a particle is totally localized, does it go faster? In Feynman's lectures on physics, volume I, section 6-5, Feynman states:
$$\Delta x\cdot \Delta v \ge h/m $$
($\Delta x$ is the width of the probability distribution of the location, $\Delta v$ is the width of the probability dist... | The argument says nothing about the average velocity of the particle, which will remain at $\langle v\rangle = 0$ for bound states; moreover, $|v|=0$ will normally still be the most likely speed in that state. Nevertheless, if you want a distribution with a very large width $\Delta v$, then it will need to have suppor... | {
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Why does gravity act at the center of mass? Sorry if this is a trivial question.
Why does gravity act at the center of mass?
If we have a solid $E$, shouldn't gravity act on all the points $(x,y,z)$ in $E$? Why then when we do problems we only only consider the weight force from the center of mass?
| The only time we need to know where a force acts is when we are calculating a torque. For contact forces, it is clear that the force acts at the point of contact. But for a force like gravity, that acts at a distance, it is less clear.
In reality, a rigid object is made up of many particles, and there is a small gravit... | {
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Queries about rotational groups $\mathrm{SO}(3)$ and $\mathrm{SU}(2)$ in QM In a QM text I am using (Sakurai 2nd edition 'Modern Quantum Mechanics'), he describes two rotation groups, namely the $\mathrm{SO}(3)$ rotation group and $\mathrm{SU}(2)$ rotation group (unitary unimodular group).
He defines $\mathrm{SO}(3)$ ... | When classifying representations of a group in QM, it is necessary to allow for projective representations, because states are actually rays (equivalence classes) in the Hilbert space. This means that in order to study the rotational symmetry of a system, you want the projective representations of $\mathrm{SO}(3)$, whi... | {
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Crash simulation on Mythbusters I remember an episode of mythbusters where they were busting myths to do with a head on collision between two cars.
They said that instead of crashing two cars into each other at 50mph they would crash a car into a stationary object at 100mph because the energy involved in the crash woul... | In first case: Total Energy $$E_1= \frac{1}{2}mv^2 + \frac{1}{2}mv^2=mv^2$$
In second case: Total Energy $$E_2=\frac{1}{2}m(2v)^2=2mv^2$$
Thus, total energy doubles i.e $$E_2=2E_1$$
| {
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Is Frobscottle from the movie 'The BFG' less dense than air? For those who have either read the book, or watched the movie "The BFG", you would know Frobscottle as a green drink the giant uses, and has bubbles fizzing "in the wrong way", which is downwards. Assuming the bubbles to be filled with air, and that gravitati... | Why assume that the bubbles are air? A mixture of xenon and oxygen in a bottle of water pressurized lower than the critical point of xenon might result in bubbles that sink. The BFG could maintain low pressure by sucking the Frobscottle out via a straw with a one-way valve.
| {
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Bell Inequalities - Expectation Values I'm currently reading Loopholes in Bell Inequality Tests of Local Realism by Jan-Ake Larsson
https://arxiv.org/abs/1407.0363
On Page 6, Equation 7, he has a short proof, where I am having a hard time seeing through the math. I'll re-state here for convenience:
$ \lvert E(A_{2}B_{... | Let's write $X$ for $A_2B_1$ and $Y$ for $A_2B_1A_1B_2$. And keep in mind that $X$ and $Y$ are each always equal to either $1$ or $-1$.
Now think of the expectation as an average. You've got a bunch of possible outcomes, and $E(X+Y)$, for example, is the average value of $X+Y$ over all those outcomes. To understand ... | {
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Friction on cars It is known that friction is given as :
$F_{friction}=\mu F_n$ , where $F_n$ is the normal force, and $\mu$ is coefficient of friction.
For a car travelling down a hill with constant velocity, the component of the gravitational force which is parallel to the cars velocity must be equal and opposite to ... | I think the misconception that arises is frictional force doesn't opposes the motion of a body but in deeper sense it opposes relative motion between two surfaces in contact which are different things. Hope it solves your problem.
| {
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How is physical information created? I am not a physist, so please forgive my ignorance. I am an avid reader of popular science though. So I read about the problem of information seemingly lost at a black hole horizon.
But my question is about the creation of the information. My limited understanding is that our Unive... | I am not a physicist either, but lately I've been entertaining new ideas relating to information, in particular. One idea is that all instruments we use to make measurements with are conspiring to give us the impression that all phenomena beyond what our senses can directly experience are really there. Like when you pu... | {
"language": "en",
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Pulley System - How the blocks will move?
I have been given the above question, with the solution,
One correction I observed from the answer was, in question c part would be acceleration of m1 and m2 are same and equal to g
Now the problem I have with the solution is that it is not in line with the string constrain... | If the acceleration of the two masses is $g$ downwards then the acceleration of pulley $A$ is $3g$ downwards, so pullet $A$ does move.
Let the centre of pulley $A$, $a$ move down a distance $x$.
On pulley $B$ the string on side $b1$ moves down $x$ and the string on side $b2$ moves up a distance $x$.
If pulley $C$ di... | {
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Talking in Space Of course, it's impossible to speak in space due to the lack of a high enough density of atoms to allow for vibrations, however, is it possible for a person's vocal chords to vibrate in outer space without any air passing through?
Furthermore, if vocal chords can still vibrate in space - would touch an... | Air passing through is what makes your vocal cords vibrate.
Also, the words that a person speaks are not formed by his/her vibrating vocal cords: It's formed by changes in the complex-shaped resonant cavity formed by the person's throat and mouth. Note how, you can understand the words that a person whispers to you, ... | {
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Quantizing one real fermion It is well-known how to canonically quantize the Lagrangian
$$L = i \bar{\psi} \dot{\psi} - \omega \bar\psi \psi$$
I now wonder how one quantizes the Lagrangian with one real fermion
$$L = i \psi \dot\psi$$
Obviously there can be no mass term since it is anticommuting so $\psi \psi = 0$.
I f... | Comments to the post (v2):
*
*Concretely, a Grassmann-odd operator $\hat{\psi}$ does not have to square to zero, cf. e.g. this Phys.SE post, even though it is true that a Grassmann-odd number $\psi$ always squares to zero: $\psi^2=0$.
*It seems OP is interested in Grassmann-odd point mechanics rather than field th... | {
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Is the event horizon of a black hole wavelength-specific? The event horizon is the boundary surrounding a black hole from which not even light can escape. There's a certain negative potential energy level associated with the event horizon. Now, some shorter-wavelength photons may have enough energy to escape the black ... | No, it's all the same.
GR does not care about the mass of something, nor does it care about its energy, when it calculates its path. It's always a geodesic and for massless particles it's always a lightlike geodesic. Makes not difference what its freq or energy is.
If it did when light is deflected by gravity, such a... | {
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Field due to internal Induced charge on a conductor to an external point? A charge q is located at a distance r from the center of a conducting sphere with inner radius 2r. The charge induces charges on the inner surface of the sphere according to Gauss' law .
The electric field at point p is to be approximated.
Inside... | Due to q charge on the sphere there will be no charge(or total charge is only at R distance from center of sphere) but at point P:
1)distance of point P from charge q is $\sqrt{17R^2}$
just use the formula of electric field for point charge then we get
$$\frac{Kq}{17R^2}$$
| {
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Measurement location on a rigid body I am just wondering if it is possible to calculate/estimate the location of measurement point on a rigid body?
For example, lets say we have a rigid body that is in motion. We attach a sensor, say an accelerometer on the surface of the rigid body. Now can we estimate the location of... | Of course this can be done: a rigid body moves, by definition, by Euclidean isomteries, i.e. its motion can be defined by a composition of a translation and a rotation of its orientation. If you know the translation of its center of mass and the rotation of its orientation, then you can work out the position of any po... | {
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Would a handspinner spin indefinitly in space? I'm having a argument with a colleague, I don't know how to explain to him that if you spin a handspinner in space it will spin indefinitly (if you don't hold it). I agree that if you hold it, it will slow down because of the friction with the center part.
Would it theoret... | Assuming a perfect vacuum, you're both partially right. The spinner would slow down due to friction with the bearing. However, this also speeds up the bearing so at some point, the entire spinner is spinning at the same rate, at which rate it would spin forever.
Furthermore, even if you do hold it, the entire spinner ... | {
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Can we theoretically "derive" the mass of a particle? I read a pop sci book on the Higgs which said that particles get their mass due to interacting with the Higgs field. If that is true, could we use first principles to derive the mass of, say, an electron? After all, QED is built on the interactions of particles and ... | We could if we'd know the coupling between the Higgs field and other particles. Instead, we use the measured mass of particles to get the value of this coupling.
| {
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Master Equation under a classical fluctuating noise I have a system as a qubit with Hamiltonian
$H_S = \frac{\Delta}{2}\sigma_z$
The interaction Hamiltonian is
$H_I = \frac{V(t)}{2}\sigma_z$ where $V(t)$ is a stochastic fluctuating variable. One can for example assume it as a random telegraph noise(RTN). In this case, ... | There is a procedure outlined here: A. A. Budini, "Non-Markovian Gaussian dissipative stochastic wave vector", Phys. Rev. A 63, 012106 (2000).
You basically take an ensemble average over the noise realizations, and use some techniques from functional calculus. It is based on Gaussian noises, but you can extend it to no... | {
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Correct definition of an 'acoustic mode'? I am reading 'The Oxford Solid State Basics' by S.H.Simon in which on page 92 defines an acoustic mode as:
... any mode that has linear dispersion as $k\rightarrow 0$.
Whilst on page 94 he defines it as:
... one mode will be acoustic (goes to zero energy at $k=0$).
Unless a... | The vibrational modes that have linear dispersion close to $k=0$ are acoustic modes where the slope of the dispersion curve is the speed of sound in the material (different for different directions of $k$).
The frequencies of optical modes do not go to zero at $k=0$. I would guess the dispersion to be quadratic.
| {
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Question regarding thermal expansion of a bi-metallic strip I was reading about bi-metallic strips and came to know that on heating it forms an arc like shape. I also read a sentence that said the radius of such an arc can also be calculated which will be taught in the future grades. So I just wanted to know if there i... | The angle subtended is given by the arc length divided by the radius:
$$\phi = \frac{L_2}{R+t/2}=\frac{L_1}{R-t/2} $$
where $L_2$ is the length of the longer strip (at $R+t/2$) and $L_1$ the length of the shorter strip (at $R-t/2$), $t$ is the thickness of the strips. $R$ is the radius to the middle of the strips. Assu... | {
"language": "en",
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How to calculate altitude from current temperature and pressure? In a certain project, I need to calculate the altitude of the current location given the current location temperature and current location pressure. Temperature, pressure and altitude of a 'reference-level' could be provided if necessary (using a fixed se... | The barometric formula is the same as the hypsometric formula if you set T=15. The reason for T+273.15 is just to put the temperature in Kelvin. This formula works to an altitude of about 9000m where the change in pressure with altitude becomes less linear.
Source: BMP180 Datasheet
| {
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Field between charged cylinders The question is the following:
"For an air-filled cylindrical capacitor, with inner radius a and outer radius b, show
that the electric field between the cylinders is
$$E = E_{in} \frac{a}{r}$$
where $E_{in}$ is the field strength at the inner cylinder and r is the distance from ... | Cylindrical capacitors have an inner radius, outer radius and also a length. So energy per unit length actually refers to the energy in a cylindrical capacitor with a unit length.
Now, the field at distance $r$ from the axis of the capacitor is $E = E_{in} \frac{a}{r}$. Thus the energy density per volume $\rho$ is g... | {
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Why is my intuition failing me in these cases? In cases where the string is rotating:
In both cases, the accelerations of both the masses along the direction of the string are different because one of them is undergoing rotation. I understand that.
But intuitively, the acceleration of two ends of a taut string along ... | The thing which is constant about an inextensible string is its length, not its shape or orientation. There is nothing which requires both ends to have the same vector acceleration, even if it is kept taut.
With the origin at the hole or pulley, the radial acceleration of each end is $a_r=\ddot r -r\dot \theta^2$. The ... | {
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Easily approximate center of mass of a person when sitting What is the simplest way to get the center of mass of a human body when sitting? I'm especially interested in getting this when sitting in a chair, so this center of mass would include the chair. I'm trying to make an exercise device for myself that attaches ... | The chair can be hanging from a self leveling short (say 6 inches vertically by 2 inches horizontally) metal strap on each side. these brackets are attached to your bar through a bolt and nut on top passing through a flange welded on the bar, providin approximately 5 inch hanging distance between the floor of the chair... | {
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Integral representation of Dirac distribution The Fourier transform of the Dirac distribution is given by
$$\tilde \delta(\vec{k}) = \frac{1}{(\sqrt{2 \pi})^3} \int_{\Bbb R^3} \delta(\vec{r})e^{-i \vec{k} \vec{r}} d^3r = \frac{1}{(\sqrt{2 \pi})^3}\tag{1}.$$
By transforming back again, we get an integral representation ... | Note that the Kronecker delta is dimensionless, while the Dirac delta has the dimensions of one-over its argument:
$$
\begin{aligned}
{}[\delta_{a,b}]&=1\\
[\delta(a-b)]&=[a]^{-1}
\end{aligned}
$$
With this, you should be able to tell if $(3)$ is a Dirac delta or a Kronecker delta. Hint: it's a Kronecker delta in disgu... | {
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Does a capacitor have a resistance? Does a capacitor have a resistance? And why? When I asked my physics teacher, he said certainly not, but I didn't figure out why. Can anyone please clarify? Thanks in advance.
| If you are dealing with a real capacitor, it has for sure parasite resistances, you may model it as follow
Where $Rs$ is the equivalent serie resistance, $Rp$ the parallel one, and the capacitor in the circuit, is intended to be an ideal capacitor which... | {
"language": "en",
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Are all atomic collisions elastic? If this is the case, why? In kinetic theory of gases it is considered all atomic collisions to be elastic. But if collisions are non-elastic the molecules must lose energy.
| The kinetic energy of a moving atom $K~=~\frac{1}{2}mv^2$ has to be comparable to the atomic levels for the collision to be inelastic. The Rydberg levels of a hydrogen atom are $E_n~=~-13.6eV/n^2$, for $n$ the atomic level. For a transition from the $N~=~2$ level to the $n~=~1$ level the energy released is $\Delta E~=~... | {
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What causes this triangle effect? (waterfall) I was in a friends garden and saw this:
My question is: what causes the water to flow towards the center? My first thought was that maybe the water in the center falls faster and thus creates a sort of force inwards, but because gravity doesn't care about weight I don't th... | In regard to the effects on the edges, by the looks of it, it is quite reasonable to think of Kelvin-Helmholtz instabilities, since there will be a shear layer between the water falling at a specific speed and the air being pulled down at a different (probably slower) speed.
| {
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How to prove the constant speed of light using Lorentz transform? I read the light-clock example in my book which proved the time dilation formula by assuming that the speed of light is constant for all observers. But I've trouble in understanding it the other way around. Lorentz transformation is just a correction to ... | We could use the relativistic velocity addition equation, which would show the speed of the light pulse to be independent of the relative motion between the two observers.
EDIT: Attached is a brief proof of the problem.
Let an observer in frame S see an object in a reference frame moving at velocity V w.r.t. S emit a p... | {
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Diverging Sound Horizon Cosmology So from my understanding the sound horizon equals
$$
r_s(z) = \frac{c}{3^{1/2}H_0}\int_z^{+\infty}{\rm d}z' \frac{1}{\sqrt{1+(3\omega_b)/(4\omega_r))(1+z')^{-1}}}
$$
However for all finite $z$ this integral diverges. Am I reading the formula in this paper wrong? (Equation 29). I omit... | There is a problem in the paper you're citing. The sound horizon is (roughly) defined as the distance that waves have propagated prior to redshift $z$
$$
r_s(z) = \int_z^{+\infty}{\rm d}z' \frac{c_s(z')}{H(z')} \tag{1}
$$
Where $c_s(z)$ is the time-dependent sound speed
$$
c_s(z) = \frac{c}{\sqrt{3(1 + R(z))}} \tag{2}... | {
"language": "en",
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Intuitive reason for the $T^4$ term in Stefan Boltzmann law The Stefan Boltzmann Law gives a relation between the total energy radiated per unit area and the temperature of a blackbody. Specifically it states that, $$ j= \sigma {T}^4$$ Now using the thermodynamic derivation of the energy radiated we can derive the abov... | There's roughly $kT$ energy in each active mode. The active modes are characterized by momenta which live inside a sphere of radius proportional to $kT$, which has volume proportional to $T^3$. Multiplying these factors gives $T^4$, and the result clearly generalizes to $T^{d+1}$ in general dimension.
| {
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What is an operator times one of its eigenstates? I am trying to get a hold of caluclating with matrix elements. I have a Hamiltionian $\hat{H}$ in a two-dimensional Hilbert space, having eigenstates $\psi_1$ and $\psi_2$. My professor wrote down these equations:
$$\hat{H} \psi_1 = H_{11} \psi_1 + H_{12}\psi_2 \\
\hat{... | The idea is that the two states $\{\psi_1,\psi_2 \}$ form a basis for the Hilbert space, this means that any other vector can be written as a linear combination of these two states, in particular the result of operating $H$ on, say, $\psi_{1}$
$$
H\psi_1 = H_{11}\psi_1 + H_{12}\psi_2 \\
H\psi_2 = H_{21}\psi_1 + H_{22}\... | {
"language": "en",
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Will a Cylinder placed on a frictionless inclined plane keep on slipping at its place or skid and slide down the plane? I've been wondering after learning about rolling without slipping and how it needs static friction for an object to start rolling but my question is that if theoretically the surface is frictionless t... |
Taking torque about COM of the disc.
Torque due to mgsinα and mgcosα is zero.
Only friction causes torque i.e. fR.
Torque due to friction causes the rolling, hence in absence of friction there is no rotation which implies that disc won't be able to attain rolling condition.
| {
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Evaluating Potential Energy Integral in Quantum Chemical Calculations My question is what are the steps for taking an integral of the following form?
$$\int e^{-\alpha|\mathbf r- \mathbf R_a|^2} {1\over|\mathbf r- \mathbf R_b|} e^{-\beta|\mathbf r- \mathbf R_b|^2} dV$$
This integral is commonly seen when attempting to ... | Here is a more formal complete solution going off the approach suggested from the comments.
$I=\int e^{-\alpha|\mathbf r-\mathbf R_a|^2} {1 \over |\mathbf r-\mathbf R_b|} e^{-\beta|\mathbf r-\mathbf R_b|^2}dV $
First changing the arrangement of the equation we can define $\mathbf \Delta \mathbf R$ and $\mathbf r'$as:... | {
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What is the accepted meaning of atomic orbitals and elementary particles in Quantum Field Theory? If elementary particles are represented as oscillations of their respective fields, why are atomic orbitals said to represent the probability of finding an electron at a specific location in the electron cloud or orbitals ... | At energy scales sufficient for the creation or destruction of particle-antiparticle pairs, we have to talk in terms of fields. At low energies, we can talk in terms of $N$-particle states because $N$ cannot change. Then wavefunctions can describe these states, e.g. Slater determinants can describe systems of identical... | {
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Can the 7-10 rule of thumb for radiation be understood theoretically? Is there a way to understand where the 7-10 Rule of Thumb for nuclear radiation comes from? A seven fold increase in time after explosion results in a 10 fold reduction in exposure rate.
From a FEMA page on responding to "nuclear threats":
From the... | As long as isotopes half-lifes are log-uniformly spread, decay of their mix will follow hyperbolic law. Actually we do not even need really good uniformity - even big random error will not break hyperbola. See my code
I suppose it is connected to the distribution of half-lives, but I have no idea how to explain in a go... | {
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Marginal and relevant operators that a $\phi^4$ theory should contain as an effective field theory Consider the Lagrangian of $\phi^4$ theory in 4-dimensions $$\mathcal{L}=\frac{1}{2}(\partial_\mu\phi)^2-\frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4\tag{1}$$ For a term in the Lagrangian of the form $C_{m,n}\phi^n(\part... | your power-counting is not correct. In $d=4$ a gradient $\partial_{\mu}$ counts like a field $\phi$. So for instance you should have $C_{m,n}'=b^{n+2m-4}C_{m,n}$
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is the quantum structure of the interstellar matter? Consider an interstellar medium of one hydrogen atom/cm$^3$ with $500$ photons/cm$^3$ coming from CMB. This density of particles is very weak according to quantum decoherence. So, according to Schrödinger equation, the wave function of each atom could be quite f... | CMB photons interact extremely weakly with interstellar matter (and with each other), so it is indeed the case that if the photons were coherent, it would take a long time for them to decohere. However, the CMB spectrum shows no coherence at all, the spectrum is a perfect black body (the most perfect black body ever ob... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/336652",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 1,
"answer_id": 0
} |
Why are there two layers of clouds? Clouds form because the warm air has risen above the cool air, and in between those two entities the water vapor condenses.
So why do there happen to be three entities - that is, one layer of air, a cloud, another layer of air, then another cloud?
For example, cirrus clouds over low... | Clouds form because the air cools enough to condense the water out of them into droplets. So if the clouds end at a certain altitude, it means that enough moisture in the air has condensed out such that the amount remaining is low enough to stay gaseous.
Sometimes this happens at low altitudes, sometimes (such as thun... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/336907",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is $\gamma^5$ used to define the projection operator? The properties of the projection operators are defined as:
$$P_+ = \frac{1}{2}(1+\gamma^5)$$
$$P_- = \frac{1}{2}(1-\gamma^5)$$
where $\gamma^5 = -i\gamma^0\gamma^1\gamma^2\gamma^3$
and their key properties are that $P_+^2 = P_+, P_+P_- = 1, P_-^2 = P_-$.
But sin... | To understand the importance of $\gamma^5$ you need to understand chirality first. Let me describe briefly. Chirality is a property of asymmetry, an object/system is called chiral if it is distinguishable from its mirror image. In other words the object can not be superposed on its mirror image just by rotations. Chira... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/337288",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
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